The Rule of 72 is a mathematical concept that is used in finance and investing as a quick way to estimate how long something takes to double in value. It works like this…

“If you divide 72 by an interest rate or a rate of return, then the result tells you the approximate amount of time (in years) that the investment would take to double in value”.

An example will illustrate how this ‘rule’ works. If an investment earns 12% per annum and if you re-invest the returns, then your original amount will double after about ’72-divided-12′ years. In other words, it would double after about 6 years. We can show this is true using a real example where you invest $1000 for 6 years:

 

Year	Start Amount $	Growth @ 12%	End Amount $
1	1,000	120	1,120
2	1,120	134	1,254
3	1,254	151	1,405
4	1,405	169	1,574
5	1,574	189	1,762
6	1,762	211	1,964

 

Note that the time-frame does not have to be in years. It could be in months, weeks or days. If you could somehow earn 12% in a month, then your investment would double after about 6 months. In our example 12 divided into 72 exactly so we came up with an answer of 6 years.

If our interest rate was 11% then that divides into 72 about 6.5 times, so in this case the investment would double after about 6.5 years (not exactly but approximately). Likewise for a rate of 13% which divides into 72 about 5.5 times – so our money would double after 5.5 years approximately.

We can use rule of 72 in many ways:

 If you get a 5% pay rise every year then it would take about 14 years for your pay to double.
 If the price of fuel rises by 10% every year, then it would take about 7 years for the price to double.

You could use it to estimate how long to invest for:
 If you wanted to double your bank balance in 25 years without adding any extra funds then it would require that you earn about 3% per annum (72 divided by 25).

The rule could have been called the rule of 70 or rule of 69 as that would give more accurate results. Actually had it been called the rule of 69.2 then that would be even more accurate. However, then it’s not very easy to make approximations and the rule-of-72 is just that – a method of approximating something.

The number 72 was chosen because it is exactly divisible by so many small numbers – 1, 2, 3, 4, 6, 8, 9, 12 and its easy to approximate dividing by 5, 7, 10, 11 as well.

 

Here is a summary of approximately how long your money takes to double for various rates of return…

 

Growth Rate	Approximate years to double
2%	36
3%	24
4%	18
5%	14
6%	12
7%	10
8%	9
9%	8
10%	7
11%	6.5
12%	6
13%	5.5

 

Use this rule of 72 next time you want to quickly evaluate or compare investments or borrowings.